To find the distance between two points, \((x_1, y_1)\) and \((x_2, y_2)\), we use the **distance formula**:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Given the points \((0, 6)\) and \((5, -2)\), let's plug the values into the formula:

\[
d = \sqrt{(5 - 0)^2 + (-2 - 6)^2}
\]
\[
d = \sqrt{5^2 + (-8)^2}
\]
\[
d = \sqrt{25 + 64}
\]
\[
d = \sqrt{89}
\]

The distance between the two points is \(\sqrt{89} \approx 9.43\) units.

Would you like more details or have any questions?

Here are 5 related questions to expand this topic:
1. What is the midpoint between the points \((0, 6)\) and \((5, -2)\)?
2. How do we find the slope of the line passing through these two points?
3. What is the equation of the line passing through \((0, 6)\) and \((5, -2)\)?
4. Can the distance formula be derived from the Pythagorean theorem?
5. How would the distance change if one or both points were moved?

**Tip:** Always visualize a coordinate plane when solving for distances, as it helps with understanding geometric relationships between points.

Learn how to calculate the distance between two points (0,6) and (5,-2) using the distance formula. This example covers key concepts in geometry, including the Pythagorean Theorem and coordinate geometry. Suitable for students in Grades 6-8.

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